Learning quantum state properties with quantum and classical neural networks

While the simulation of quantum systems on near-term quantum devices have witnessed rapid advances in recent years, it is only the first step in understanding these systems. The efficient extraction of useful information from a simulated state represents a second important challenge. The traditional technique is to reconstruct the state using quantum state tomography before analytically computing the desired properties. However, this process requires, in general, an exponential number of measurements and it is inherently inefficient if we are not interested in the state itself, but only in a handful of scalar properties that characterize it. In this thesis, we introduce several quantum algorithms to estimate quantum state properties directly without relying on tomography. The algorithms are a combination of quantum and classical neural networks, trained to return the desired property. Our contribution is both theoretical and numerical: we prove the universality of several architectures for the class of properties given as polynomial functionals of a density matrix, and evaluate their performance on some particular properties— purity and entropy—using quantum circuit simulators. Furthermore, we provide an extension of each architecture for continuous-variable states.